\(1,2-2,2+3,2-4,2+5,2-6,2+...+22,2-23,2+24,2\)

\(=\left(1,2-2.2\right)+\left(3,2-4,2\right)+\left(5,2-6,2\right)+...+\left(22,2-23,2\right)+24,2\)

\(=\left(-1\right)+\left(-1\right)+\left(-1\right)+...+\left(-1\right)+24,2\)

\(=\left(-1\right).23+24,2\)

\(=\left(-23\right)+24,2\)

\(=1,2\)

\(4746+765=5511\)

\(B=\dfrac{1}{6}+\dfrac{1}{6^2}+\dfrac{1}{6^3}+...+\dfrac{1}{6^{2023}}+\dfrac{1}{6^{2024}}\)

\(6B=1+\dfrac{1}{6}+\dfrac{1}{6^2}+...+\dfrac{1}{6^{2022}}+\dfrac{1}{6^{2023}}\)

\(6B-B=\left(1+\dfrac{1}{6}+\dfrac{1}{6^2}+...+\dfrac{1}{6^{2022}}+\dfrac{1}{6^{2023}}\right)-\left(\dfrac{1}{6}+\dfrac{1}{6^2}+\dfrac{1}{6^3}+...+\dfrac{1}{6^{2023}}+\dfrac{1}{6^{2024}}\right)\)

\(5B=1-\dfrac{1}{6^{2024}}\)

\(B=\dfrac{1}{5}-\dfrac{1}{5.6^{2024}}< \dfrac{1}{5}\)

\(\Rightarrow B< \dfrac{1}{5}\)

Góc A,B là góc tù

Góc C là góc nhọn

\(A=\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+\dfrac{1}{7.8}+...+\dfrac{1}{59.60}\)

\(A=1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{7}-\dfrac{1}{8}+...+\dfrac{1}{59}-\dfrac{1}{60}\)

\(A=\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{60}\right)-2\left(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{8}+...+\dfrac{1}{60}\right)\)

\(A=\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{60}\right)-\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{30}\right)\)

\(A=\dfrac{1}{31}+\dfrac{1}{32}+\dfrac{1}{33}+...+\dfrac{1}{60}\)

Ta tách A thành 3 nhóm\(A=\left(\dfrac{1}{31}+\dfrac{1}{32}+...+\dfrac{1}{40}\right)+\left(\dfrac{1}{41}+\dfrac{1}{42}+...+\dfrac{1}{50}\right)+\left(\dfrac{1}{51}+\dfrac{1}{52}+...+\dfrac{1}{60}\right)\)\(A>\dfrac{1}{40}.10+\dfrac{1}{50}.10+\dfrac{1}{60}.10\)

\(A>\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}\)

\(A>\dfrac{37}{60}>\dfrac{7}{12}\)

\(\Rightarrow A>\dfrac{7}{12}\)

\(D=1-3+5-7+...+2017-2019+2021\)

\(D=\left(1-3\right)+\left(5-7\right)+...+\left(2017-2019\right)+2021\)

\(D=\left(-2\right)+\left(-2\right)+...+\left(-2\right)+2021\)

\(D=\left(-2\right).1010+2021\)

\(D=\left(-2020\right)+2021\)

\(D=1\)

\(A=\dfrac{12}{\left(2.4\right)^2}+\dfrac{20}{\left(4.6\right)^2}+...+\dfrac{388}{\left(96.98\right)^2}+\dfrac{396}{\left(98.100\right)^2}\)

\(A=\dfrac{1}{2^2}-\dfrac{1}{4^2}+\dfrac{1}{4^2}-\dfrac{1}{6^2}+...+\dfrac{1}{96^2}-\dfrac{1}{98^2}+\dfrac{1}{98^2}-\dfrac{1}{100^2}\)

\(A=\dfrac{1}{2^2}-\dfrac{1}{100^2}\)

\(A=\dfrac{1}{4}-\dfrac{1}{100^2}< \dfrac{1}{4}\)

\(\Rightarrow A< \dfrac{1}{4}\)

\(5m4dm=54dm\)

\(\dfrac{2x+1}{-27}=\dfrac{-3}{2x+1}\)

\(\Leftrightarrow\left(2x+1\right)\left(2x+1\right)=\left(-3\right)\left(-27\right)\)

\(\Leftrightarrow\left(2x+1\right)^2=81\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+1=9\\2x+1=-9\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-5\end{matrix}\right.\)

\(\left(2x-3\right)\left(\dfrac{5}{4}x-6\right)=0\)

\(\Rightarrow2x-3=0\) hoặc \(\dfrac{5}{4}x-6=0\)

\(\Rightarrow x=\dfrac{3}{2}\) và \(x=\dfrac{24}{5}\)